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2 years ago

Three-fourths of the difference of a number and 7 is negative fifteen. The number is _______

Mathematics

1 answer:

Vsevolod [243]2 years ago

4 0

Answer:

x = -13

Step-by-step explanation:

Let the number be x. ATQ,

$\dfrac{3}{4}(x-7)=-15$

The above equation shows Three-fourths of the difference of a number and 7 is negative fifteen. We need to find the number.

cross multiplying both sides,

$3(x-7)=-60\\\\x-7=-20\\\\x=-20+7\\\\x=-13$

So, the number is -13.

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Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?

Olegator [25]

When the concentration of a solution is expressed in weight percentages, that is just equal to the mass of solute over the mass of the total solution. For a solution weighing 210 grams, 5% of it is salt. That is equal to

210*0.05= 10.5 g salt

The rest of the amount, determined by difference, is the amount of solvent which is water.

water = 210-10.5 = 199.5 g salt

To solve for the new concentration, you add up 15 g to the already existing 10.5 g of salt in the solution. The water, on the other hand, remains constant.

Concentration = (15+10.5)/(210+15) = 0.1133 or 11.33%

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2 years ago

Plz help and if you don't answer correctly i will report

KIM [24]

Answer:

1st, 3rd, 4th, 2nd

Step-by-step explanation:

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2 years ago

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The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. The equation of the circle

Furkat [3]

For an equation to pass through the origin, (0,0) must be a solution of the equation. So, for the first one,

$(x + 12)^{2} + (y + 16)^{2} = r_{1}^{2}$

(0, 0) must satisfy the equation and we can solve for the value of r₁ as shown below.

$(0 + 12)^{2} + (0 + 16)^{2} = r_{1}^{2}$
$12^{2} + 16^{2} = r_{1}^{2}$
$r_{1} = \sqrt{12^{2} + 16^{2}}$
$r_{1} = 20$

Since the second equation of the circle also passes through the origin, we use the same steps from the first one.

$(0 - 30)^{2} + (0 - 16)^{2} = r_{2}^{2}$
$r_{2} = \sqrt{30^{2} + 16^{2}}$
$r_{2} = 34$

Thus, we have the values for r₁ and r₂ as 20 and 34, respectively.

Answer: r₁ = 20 and r₂ = 34

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2 years ago

One of the tallest buildings in a country is topped by a high antenna. The angle of elevation from the position of a surveyor on

irina1246 [14]

Answer:

a. distance of the surveyor to the base of the building = 2051.90 ft

b. height of the building = 1384 ft

c. Angle of elevation from the surveyor to the top of the antenna = 38.31°

d. Height of antenna = 237.08 ft

Step-by-step explanation:

The picture above is a illustration of the described event.

a = the height of the flag

b = the height of the building

c = distance of the surveyor from the base of the building

the angle of elevation from the position of the surveyor on the ground to the top of the building = 34°

distance from her position to the top of the building = 2475 ft

distance from her position to the top of the flag = 2615 ft

(a) How far away from the base of the building is the surveyor located?

using the SOHCAHTOA principle

cos 34° = c/2475

c = 0.8290375726 × 2475

c = 2051.8679921

c = 2051.90 ft

(b) How tall is the building

The height of the building = b

sin 34° = opposite /hypotenuse

0.5591929035 = b/2475

b = 0.5591929035 × 2475

b = 1384.0024361

b = 1384.00 ft

(c) What is the angle of elevation from the surveyor to the top of the antenna?

let the angle = ∅

cos ∅ = adjacent/hypotenuse

cos ∅ = 2051.90/2615

cos ∅ = 0.784665392

∅ = cos-1 0.784665392

∅ = 38.310258303

∅ = 38.31°

(d) How tall is the antenna?

height of the antenna = a

sin 38.31° = opposite/hypotenuse

sin 38.31° = (a + b)/2615

sin 38.31° × 2615 = (a + b)

(a + b) = 0.6199159917 × 2615

(a + b) = 1621.0803182

(a + b) = 1621. 08 ft

Height of antenna = 1621. 08 - 1384.00 = 237.08031822 ft

Height of antenna = 237.08 ft

8 0

2 years ago

Fernando evaluated the expression below. StartFraction 5 (9 minus 5) over 2 EndFraction + (negative 2) (negative 5) + (negative

Rzqust [24]

Answer:

Fernando incorrectly found the product of –2 and –5.

Step-by-step explanation:

Fernando evaluated the numerator of the fraction incorrectly.

Fernando simplified StartFraction 20 over 2 EndFraction incorrectly.

Fernando incorrectly found the product of –2 and –5.

Fernando evaluated (negative 3) squared incorrectly.

Fernando's calculation

5(9-5) / 2 + (-2)(-5) + (-3)^2

= 5(4) / 2 - 10 + 9

= 20/2 - 10 + 9

= 10 - 10 + 9

= 9

Correct calculation

5(9-5) / 2 + (-2)(-5) + (-3)^2

= 5(4) / 2 + (10) + 9

= 20/2 + 10 + 9

= 10 + 10 + 9

= 29

Therefore,

Fernando's error was multiplying (-2)(-5) to be equal to -10 instead of 10

Fernando incorrectly found the product of –2 and –5.

5 0

2 years ago

Read 2 more answers

Three-fourths of the difference of a number and 7 is negative fifteen. The number is _______​

Three-fourths of the difference of a number and 7 is negative fifteen. The number is _______