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Quick algebra 1 questions

The value of the angle ∠BCA when approximated to 3 significant figures is;  20.4°

From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.

Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;

x/y = sin BCA

Plugging in the relevant values gives us;

8/23 = sin BCA

∠BCA = sin⁻¹(8/23)

∠BCA = 20.355

Approximating to 3 significant figures gives us;

∠BCA = 20.4°

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The value of x is 8.5 cm

The complete question is in the image

The given parameters are:

y = 12 cm

[tex]\theta = 45^o[/tex]

The value of x is calculated using the following sine ratio

[tex]\sin(\theta) = \frac xy[/tex]

This gives

[tex]\sin(45^o) = \frac x{12}[/tex]

Multiply by 12

[tex]x = 12 * \sin(45^o)[/tex]

Evaluate

x = 8.5

Hence, the value of x is 8.5 cm

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Answer:

2.50x+1.25y=z

Step-by-step explanation:

Let the number of juice bottles = x

And the number of containers of popcorns=y

And the total number of juice bottles and containers of popcorns=z

Total number of juice bottles=x times $2.50

Total number of containers of popcorn= y times $ 1.25

equation; 2.50x+1.25y=z

Answer:

[tex] \frac{8}{24} [/tex]

Step-by-step explanation:

If Adam's family uses 8lb of apples to make pie. We know that 3 x 8 = 24, so it's probably approximately 3 out of 18.

Answer:

10

Step-by-step explanation:

Plugin your answer: -4 + 10 = 6

Answer:

10

Step-by-step explanation:

Answer:

Not similar

Step-by-step explanation:

There is only one side and one angle, which insufficient to prove triangle similarity.

Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

Writing an Equation to Represent a Proportional Relationship

What is proportional relationship?

A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.

Going back to the given problem above, we have the table showing the proportional relationship between j and m.

j | 4 | 12 | 20 |

m | 3 | 9 | 15 |

Solution:

Step #1

The proportional relationship can be written as:

m/j = ¾ = ‌9⁄12‌ = ‌15⁄20‌ = ¾

Step #2

So, the equation representing this proportional relationship is:

m = ¾ × j/1 = 3j/4

Final Answer:

The equation representing the proportional relationship between j and m is m = 3j/4 .

Step-by-step explanation:

The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time

An equation is an expression that shows the relationship between two or more numbers and variables.

The distance travelled in 30 minutes is:

Distance = speed * time = 4 mph * 0.5 h = 2 miles

The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time

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Answer:

f(x)=2x-3

Step-by-step explanation:

cause fir example if you put x=2 the y became 1.

Answer:

[tex]D[/tex]

Step-by-step explanation:

Notice that the red graph does not globally differ from the black graph: it would have been approximately the same one unless it had been displaced by 3 units up. Therefore, it was only the ordinate axis that underwent our change: [tex]y - 3 = f(x) \Leftrightarrow y = f(x) + 3[/tex].

Answer:

C

Step-by-step explanation:

Answer:

1/49.

Step-by-step explanation:

(−7)^-2

=  1 /(- 7)^2

= 1/49.

Answer:

choice C

Step-by-step explanation:

The circle is circumscribed because circles drawn on the outside is known as circumscription. The circle is clearly outside touching the three vertices of the triangle.

Answer:

32...................

The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)

An equation is an expression that shows the relationship between two or more variables and numbers.

The surface area of  pyramid = sum of individual area of the surface

Surface area = (2 * 2) + 4(0.5 * 2 * 3)

The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)

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The linear equation that best fits the data is: y = 10x + 15.

First, find the slope/unit rate (m) and the y-intercept/starting value, then substitute the values into y = mx + b.

Using two points on the graph, (1, 25) and (2, 35), find the slope (m):

Slope (m) = (35 - 25)/(2 - 1)

Slope (m) = 10/1

Slope (m) = 10

Substitute (x, y) = (1, 25) and m = 10 into y = mx + b to find b

25 = 10(1) + b

25 - 10 = b

b = 15

Substitute m = 10 and b = 15 into y = mx + b

y = 10x + 15

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Substituting L = 7.29,

[tex]t = 2.01 \sqrt{7.29} \approx \boxed {5.4}[/tex]

Answer:

Step-by-step explanation:

Maybe..

8/10

12/15

16/20

20/25

24/30

28/35

32/40

36/45

40/50

Any one of these is equal to the ratio of 4 over 5.

Answer:

No, the person who answered first is wrong

I'll give you the correct answer

Step-by-step explanation:

He the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

thank you, this is the correct answer

hope that hepls

Answer:

CD = 13

Step-by-step explanation:

since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so

CD = DA = 13

Answer:

13

Step-by-step explanation:

We know that if two triangles are congruent, the corresponding element of those are also equal.

Given that,

ABD Δ ≡ CBD Δ

Therefore, the corresponding elements are also equal.

AD = CD

AD = 13 units

∴ CD = 13 units

Using a linear function, it is found that you would need roughly 24 hours of training to have a monthly pay of $1500.

A linear function is modeled by:

y = mx + b

In which:

Looking at the table, the pay increases $200 each 10 hours of work, hence the slope is:

m = 200/10 = 20

Then:

y = 20x + b

When x = 10, y = 1220, hence:

y = 20x + b

1220 = 20(10) + b

b = 1020.

Then the pay for x hours of training is:

y = 20x + 1020.

For a pay of $1500, we have that:

y = 20x + 1020.

1500 = 20x + 1020.

20x = 480

x = 24

You would need roughly 24 hours of training to have a monthly pay of $1500.

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If m has exactly 5 positive divisors then there can only be one prime factor.

According to statement

m has exactly 5 positive divisors AND

Let A^p,B^q,.... are the possible factors of integer m then

assume that p and q ≥ 1.

then the number of possible divisors cannot be 5 because there are no two integers  p, q ≥ 1, such that (p +1)(q + 1) = 5

So, If m has exactly 5 positive divisors then there can only be one prime factor.

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The statement, m∠4 = m∠5, then then r||s is true based on the converse of corresponding angles theorem.

Based on the converse of corresponding angles theorem, if two corresponding angles, angles 4 and 5 are congruent or equal to each other, then the lines on which they lie on, lines r and s are congruent.

Therefore, based on the converse of corresponding angles theorem, m∠4 = m∠5, then then r||s.

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Answer:

10

Step-by-step explanation:

This is because you would have to start with 109 = 23x

then solve it using logarithms

Then once you get the x value, it becomes

X>_10__(whatever number you found)

Step-by-step explanation:

The expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and  53(1.75)(0.3)^x

An exponential function is represented as:

y = ab^x

The above means that options (f) and (g) are not exponential functions

When b is less than 1, then the function is an exponential decay.

From the list of options, we have:

900(0.05)^t => b = 0.05

700(0.9)^x => b = 0.9

53(1.75)(0.3)^x => b = 0.3

Hence, the expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and  53(1.75)(0.3)^x

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A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.

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

The car is 120 miles away when the motorcycle starts.

The bike gains on the car at 30 mph (70-40).

It takes 4 hours for the bike to close the gap (120/30).

In 4 hours, the bike and the car are 280 miles from the starting point.

---------

4*70 = 280

7*40 = 280

Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.

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The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The value of x, y and z is 90°, 53°, and 100°, respectively.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

In ΔABD is made on the diameter of the circle, therefore, the measure of ∠BAD = 90°. Therefore,

x° = 90°

In ΔAOD, the measure of ∠AOD is 74°, also, the triangle is an isosceles triangle with OA and OD of equal length. Therefore, the sum of the angles can be written as,

y° + y° + 74° = 180°

2y° = 106°

y = 53°

Similarly, ΔBOC is an isosceles triangle with OB and OC having an equal length. Therefore, ∠OBC=∠OCB. Also, the sum of all the angles can be written as,

∠BOC + ∠OBC + ∠OCB = 180°

∠BOC + 40° + 40° = 180°

∠BOC = 100°

Hence, the value of x, y and z is 90°, 53°, and 100°, respectively.

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