All categories

2 years ago

AB is the angle bisector of CAD. Solve for the missing variable?

Mathematics

1 answer:

Alika [10]2 years ago

4 0

Answer:

$x=8^\circ$

Step-by-step explanation:

A bisector is the line that divides an angle (which in this case is $\angle CAD$ ) exactly in half. Therefore, $\angle CAB = \angle BAD$ and as such we can solve for $x$ :

$\angle CAB &= \angle BAD\\33^\circ &= 4x + 1^\circ\\4x = 32^\circ\\x = 8^\circ$

and we are done.

You might be interested in

Please help with geometry,will give brainliest

wolverine [178]

Answer:

Step-by-step explanation:

i think

8 0

2 years ago

We have a jar of coins, all pennies and dimes. All together, we have 309 coins, and the total value of all coins in the jar is $

Vinvika [58]

There are 130 pennies in the jar

Step-by-step explanation:

We have a jar of coins

All coins are pennies and dimes
There are 309 coins in the jar
The total value of all coins in the jar is $ 19.2

We need to find the number of pennies in the jar

Assume that there are p pennies and d dimes in the jar

∵ There are p pennies and d dimes in the jar

∵ There are 309 coins in the jar

∵ All the coins in the jar are pennies and dimes

∴ p + d = 309 ⇒ (1)

∵ The total value of all coins in the jar is $ 19.2

∵ $1 = 100 cents

∴ $19.2 = 19.2 × 100 = 1920 cents

∵ 1 penny = 1 cent

∵ 1 dime = 10 cents

∴ p + 10 d = 1920 ⇒ (2)

Now we have system of equations, we can solve them to find p

∵ p + d = 309 ⇒ (1)

∵ p + 10 d = 1920 ⇒ (2)

- Multiply equation (1) by -10 to eliminate d

∵ (-10)(p) + (-10)(d) = (-10)(309)

∴ -10 p - 10 d = -3090 ⇒ (3)

Add equations (2) , (3)

∴ -9 p = -1170

- Divide both sides by -9

∴ p = 130

There are 130 pennies in the jar

Learn more:

You can learn more about the system of equations in brainly.com/question/3739260

#LearnwithBrainly

8 0

2 years ago

Ms. Cruz has a tank with 11 fish. After buying two more, she has 2 less than triple the amount of fish Ms. Montesinos has. How m

notka56 [123]

Answer:

a) The variable, M represents the amount of fish Ms. Montesinos has

b) The set equation is 11 + 2 = 3 × M - 2

c) 5

Step-by-step explanation:

The given parameters are;

The number of fishes in Ms. Cruz's tank = 11 fishes

The number of fishes Ms, Cruz has after buying two more fishes = 3 × The amount of fish Ms. Montesinos has - 2 fishes

a) Let the variable, M represent the amount of fish Ms. Montesinos has

b) The set up equation is as follows;

11 + 2 = 3 × M - 2

c) From the equation, 11 + 2 = 3 × M - 2, we have;

13 = 3·M - 2

3·M = 13 + 2 = 15

3·M = 15

M = 15/3 = 5

M = 5

The number of fishes Ms. Montesinos has is 17 fishes

5 0

2 years ago

Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.

Vinvika [58]

Answer:

The point estimate for population mean is 8.129 Mpa.

Step-by-step explanation:

We are given the following in the question:

Data on flexural strength(MPa) for concrete beams of a certain type:

11.8, 7.7, 6.5, 6.8, 9.7, 6.8, 7.3, 7.9, 9.7, 8.7, 8.1, 8.5, 6.3, 7.0, 7.3, 7.4, 5.3, 9.0, 8.1, 11.3, 6.3, 7.2, 7.7, 7.8, 11.6, 10.7, 7.0

a) Point estimate of the mean value of strength for the conceptual population of all beams manufactured

We use the sample mean, $\bar{x}$ as the point estimate for population mean.

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$\bar{x} = \dfrac{\sum x_i}{n} = \dfrac{219.5}{27} = 8.129$

Thus, the point estimate for population mean is 8.129 Mpa.

4 0

2 years ago

Alaina colors 20% of the total shapes on her paper. She colors 10 shapes. Enter the number of shapes on Alaina's paper.

Mashutka [201]

Answer:

Step-by-step explanation:20*5=100 so 10*5=50

3 0

2 years ago