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Doss [256]
3 years ago
5

Tuesday's high temperature was 8*C.the low temperature was -1*C .what was the difference between the high and low temperature

Mathematics
1 answer:
arsen [322]3 years ago
5 0

the difference between both of them is 9*C

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What is the slope and y-intercept of y = 1/4x + 8
icang [17]

Answer:

slope: 1/4x, Y intercept: 8

8 0
3 years ago
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The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte
malfutka [58]

1. The area of the rhombus can be found by the formula

A=\dfrac{d_1\cdot d_2}{2}, where d_1,\ d_2 are rhombus's diagonals.

Note that d_1=4.5\ dm=45\ cm, then

540=\dfrac{45\cdot d_2}{2},\\ \\540\cdot 2=45d_2,\\ \\d_2=24\ cm.

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

\dfrac{d_1}{2}=22.5\ cm,\ \dfrac{d_2}{2}=12\ cm.

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

\text{rhombus's side}^2=(22.5)^2+12^2=506.25+144=650.25,\\ \\\text{rhombus's side}=25.5\ cm.

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

(25.5-x)^2+h^2-x^2-h^2=22.5^2-12^2,\\ \\650.25-51x=506.25-144,\\ \\51x=650.25-362.25=288,\\ \\x=\dfrac{96}{17}\ cm.

Then

h^2=144-\left(\dfrac{96}{17}\right)^2=144-\dfrac{9216}{289}=\dfrac{32400}{289},\\ \\h=\dfrac{180}{17}\ cm.

Answer: h=\dfrac{180}{17}\ cm.

7 0
3 years ago
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Y2 + 15y + 56 = (y + 7)(y +
Luda [366]
19y+63 is the correct answer
6 0
3 years ago
The perimeter of the quadrilateral below is 64 units.
Harrizon [31]

Answer:

a = 22

x = 96

y = 144

Step-by-step explanation:

In the given figure

∵ The figure is a quadrilateral

∵ Each two adjacent have the same mark

∴ Every two adjacent sides are equal

∵ The perimeter of the quadrilateral is the sum of its outline sides

∴ The perimeter of the quadrilateral = 10 + 10 + a + a

∴ The perimeter of the quadrilateral = 20 + 2a

∵ The perimeter of the quadrilateral = 64 units

→ Equate the right sides of the perimeter

∴ 20 + 2a = 64

→ Subtract 20 from both sides

∵ 20 -20 + 2a = 64 - 20

∴ 2a = 44

→ Divide both sides by 2 to find a

∴ a = 22

<em>If a line segment joins the vertex of measure y and the vertex of measure 24°, then it will divide the quadrilateral into 2 congruent triangles by the SSS case.</em>

→ Use the result of congruency to find x

∵ The opposite angles of measures x and 96° are equal

∴ x = 96

∵ The sum of the measures of the angle of a quadrilateral is 360°

∴ 96° + y° + 96° + 24° = 360°

→ Add the like terms on the left side

∵ (96 + 96 + 24) + y = 360

∴ 216 + y = 360

→ Subtract 216 from both sides

∵ 216 - 216 + y = 360 - 216

∴ y = 144

6 0
3 years ago
-4 times a number plus 16 is -116. find the number and show work.
pav-90 [236]
-4*25 = -100+16 = -116
6 0
3 years ago
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