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4 years ago

Solve the inequality –24 ≤ x – 3 – 8x.

Mathematics

1 answer:

o-na [289]4 years ago

6 0

-24 ≤ x- 3 -8x
+3 +3
-21 ≤ x - 8x
-21 ≤ -7x
/-7 /-7

x ≤ 3

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To make 4.5 cups of fruity granola, the recipe calls for 1.5 cups of raisins, 1 cup of granola, and 2 cups of blueberries. If yo

Levart [38]

Answer:

you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

Step-by-step explanation:

Step 1: Find how much raisins are needed

For 4.5 cups of fruity granola, we need 1.5 cups of raisins

For 18 cups of fruity granola, we need y cups of raisins

4.5 : 1.5

18 : y

Cross multiply

4.5y = 1.5 x 18

y = 27/4.5

y = 6 cups of raisins

Step 2: Find how much granola is needed

For 4.5 cups of fruity granola, we need 1 cup of granola

For 18 cups of fruity granola, we need y cups of granola

4.5 : 1

18 : y

Cross multiply

4.5y = 18

y = 4 cups of granola

Step 3: Find how much blueberries are needed

For 4.5 cups of fruity granola, we need 2 cups of raisins

For 18 cups of fruity granola, we need y cups of blueberries

4.5 : 2

18 : y

Cross multiply

4.5y = 2 x 18

y = 36/4.5

y = 8 cups of blueberries

Therefore, in order to make 18 cups of fruity granola, you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

5 0

4 years ago

The bearing of Q from P is 150

Lynna [10]

Answer:

(i) see first attached diagram

(ii) QR = 22.67 km (2 dp)

(iii) 243°

Step-by-step explanation:

A bearing is the angle in degrees measured clockwise from north.

Part (i)

see first attached diagram

Part (ii)

The angles marked in blue on the second attached diagram are Consecutive Interior Angles. In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

Part (iii)

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

8 0

2 years ago

Cone B is the image of cone A after dilation by a scale factor of \frac{1}{2}

Bogdan [553]

The surface area of cone B is 10 km², and Cone B is the image of cone A after dilation by a scale factor of 1/2

<h3>What is an equation?</h3>

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

Cone B is the image of cone A after dilation by a scale factor of 1/2, hence:

Surface area of cone B = 40 km² * (1/2)² = 10 km²

The surface area of cone B is 10 km², and Cone B is the image of cone A after dilation by a scale factor of 1/2

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0

2 years ago

How do you solve (7^-1)^-1 and 5^2 * 5^4 * 5^-3

Katyanochek1 [597]

Answer:

Step-by-step explanation:

exponents raised to a - power is an inverse function probably not the right word

a^-b = 1/(a^b) example 4^-2 = 1/(4^2) = 1/16

so (7^-1)^-1 is a double inverse which is back to the original number 7

inverted 7 twice

(7^-1)^-1 = (1/7)^-1 = 1/(1/7) = 7 trust me or use your calculator

since the coeffients are the same just add the powers... some exponent rule

5^2 * 5^4 * 5^-3 = 5^(2+4-3) = 5³

here is it written out

5^2 * 5^4 * 5^-3 = 5² × 5^4 × 5^-3 = (5×5) × (5×5×5×5) × (1/5×1/5×1/5)

5×5 × 5× (5×5×5 × 1/5×1/5×1/5) (5×5×5 × 1/5×1/5×1/5) = 1

5×5×5 = 5³

7 0

3 years ago

how to solve the question Ms.H and 5 of her friends went out to dinner .The total bill came to $143.40 and they split evenly.The

Anton [14]

So 6 people split 143.40. 143.40/6 = 23.90. Thats how much each person paid for the dinner. Add the 7.50 they paid for the movie and you would get 31.40$ total for each person. If this is right could I possibly have brainliest? Hope this helped!! :)

7 0

3 years ago

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