h(t)=−(t−7)²+4

Write the smaller t first, and the larger t second.

smaller t=?

larger t=?


2) What is the vertex of the parabola?

(?,?)

Answer:

0.922

Step-by-step explanation:

→ State the distribution

X ~ N ( 1000 , 100² )

→ State the required probability

p ( 840 < x < 1200)

→ Enter upper bound as 1200 and lower as 840 on the normal cumulative distribution

0.922

The percentage of the rectangle that will be beige is 15.5 percent

A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The width of the "H" is 1/2 the distance form the top to the bottom of the "H" is 1/2

1/2 + 1/2 =

the side length of the "H" is 4

4 x 1/2 = 2

The demensions of the other 1/2 by 4 are the same, therefore,

2 + 2 = 4

The middle section is 1 by 1/2

1 x 1/2 = 1/2

The equation is 2 + 1/2 = 2 1/2

and converted to decimal form it is 4.5

The rectangle is 4 by 5

So 4 x 5 = 20

20 - 4.5 = 15.5 percent

Hence the percentage of the rectangle that will be beige is 15.5 percent.

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Answer:

a. Solve the System of Equations. Show your work

Answer:

A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

Answer:

it's a bit hard to see in green.

Answer:

Step 1: Create a net for the triangular prism by "cutting" two edges of the triangular faces and unfolding.

Step 2: Find the area of each triangle. Find the area of the rectangle.

Step 3: Add all areas from step 2 together. This is the surface area.

Step-by-step explanation:

Answer:

the answer is B.

Step-by-step explanation:

the formula for circumference of a circle is [tex]\pi[/tex]×diameter=C

[tex]\pi[/tex]·8=25.13

[tex]\pi[/tex]·4=12.56

12.56·2=25.13

Answer:2

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

See here the net seems like a equilateral triangle

Hence option C

The triangle VNH is an isosceles triangle because the lengths of sides VH and NH are congruent

The coordinates are given as:

V = (3,6)

N = (8,1)

H = (1,-1)

Calculate the distance between each point using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]VN = \sqrt{(8 -3)^2 + (1 -6)^2}[/tex]

[tex]VN = \sqrt{50}[/tex]

[tex]VH = \sqrt{(1 -3)^2 + (-1 -6)^2}[/tex]

[tex]VH = \sqrt{53}[/tex]

[tex]NH = \sqrt{(8 -1)^2 + (1 +1)^2}[/tex]

[tex]NH = \sqrt{53}[/tex]

Notice that two sides of the triangle are equal.

Hence, the triangle VNH is an isosceles triangle

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Answer:

-> Supplementary

-> Add up to 180°

Explanation:

       A straight line has a measurement of 180°. Supplementary angles are angles that, when added together, equal 180°.

       Since angles 5 and 6 make up a straight line, we know they will add up to 180°.

so you would ski down the mountain to the nearest foot is 2556.06ft

The volume in cm 112098 cm³.

The volume of water in liters 112 liter.

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder.

Given: height= 28m= 2800cm, internal radius= 3.5 cm, external radius = 5 cm.

Volume of cylinder

= πr²h

= 3.14(5²-3.5²)2800

=3.14*12.75*2800

=112098 cm³

Volume of water in liter is 112.098 or 112 liter.

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A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. The ratio of the height of pyramid A to pyramid B is 0.064.

A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. A lateral face is formed by the base edge and top of each triangle.

The volume of a pyramid is given by the formula,

Volume of the pyramid = (Length×Width×Height)/3

                                       = (Area of base ×Height)/3

If the area of the base of the two pyramids is the same, then the ratio of the volume of the two pyramids will be,

[tex]\dfrac{\text{Volume of Pyramid A}}{\text{Volume of Pyramid B}} = \dfrac{60\rm\ mm^3}{937.5\rm\ mm^3}\\\\\\\dfrac{3 \times \text{(Area of base})_a \times h_a}{3 \times \text{(Area of base})_b \times h_b}= \dfrac{60}{937.5}\\\\\\\dfrac{h_a}{h_b} = 0.064[/tex]

Hence, the ratio of the height of pyramid A to pyramid B is 0.064.

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Answer:

3k

Step-by-step explanation:

8k and 5k are "like terms" because they have the same variable to the same degree. So because the are like terms they can be subtracted. Similarly to how 8-5 is 3,

8k - 5k is 3k

Answer:

EK = 8

Step-by-step explanation:

Intersecting Chords Formula:  a • b = c • d

BK * KD = EK * KC

4 * 10 = (x+1) * (x-2)

40 = x^2 +x-2x-2

40 = x^2 -x -2

0 = x^2 - x-2-40

0 = x^2 -x -42

Factor

0 = (x-7) (x+6)

Using the zero product property

x-7 = 0   x+6 =0

x=7        x=-6

X is not negative

x=7

EK = x+1

EK = 7+1

EK = 8

Answer:

If this is your question: john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?

Answer:

John: 19

Jack: 9

Step-by-step explanation:

Hope it helps! God bless!

Answer:

∠ A = 140° , ∠ B = 30° , ∠ C = 10°

Step-by-step explanation:

the sum of the 3 interior angles = 180°

sum the given angles and equate to 180

x - 5 + 2x + 140 = 180

3x + 135 = 180 ( subtract 135 from both sides )

3x = 45 ( divide both sides by 3 )

x = 15

then

∠ A = 140°

∠ B = 2x = 2 × 15 = 30°

∠ C = x - 5 = 15 - 5 = 10°

Answer:

Step-by-step explanation:

Find the measures of the interior angles of the triangle.

180 = 140 + 2x + x - 5

40 + 5 = 3x

45 = 3x

x = 45 : 3

x = 15°

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

check

180 = 140 + 2 * 15 + 15 - 5

180 = 180

the answer is good

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

Find the angles

140° = angle A

2x = 15 * 2

2x = 30° (angle B)

x - 5 = 15 - 5

x = 10° (  angle C)

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

check

140 + 30 + 10 = 180°

the answer is good

Answer:

Step-by-step explanation:

Parabola:

   [tex]\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5[/tex]

[tex]\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}[/tex]

x = 7

Now, to find the y-value substitute this in the equation

               [tex]\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}[/tex]

[tex]\boxed{Vertex(7 ,\dfrac{39}{2})}[/tex]

b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.

             [tex]\sf \boxed{Maximum \ value= \dfrac{39}{2}}[/tex]

[tex]\sf c) Range = [\dfrac{39}{2}, -infinity)[/tex]

Answer:

(a) (7,39/2)

(b) Maximum, 39/2

(c) y ≤ 39/2

(d) Increase when x < 7 and decrease when x > 7

Step-by-step explanation:

Given the parabola:

[tex]\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}[/tex]

( A ) Find the vertex

In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:

Power Rules

[tex]\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}[/tex]

Derivative Definition

Derive the parabola:

[tex]\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}[/tex]

Since vertex has slope = 0 —> e.g f'(x) = 0:

[tex]\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}[/tex]

Substitute x = 7 in f(x):

[tex]\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}[/tex]

Therefore, the vertex is at (7,39/2)

( B ) Determine if max or min then find the value

Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:

( C ) Find range

For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:

[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]

( D ) Find the interval when function is increasing and when it’s decreasing

For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.

We know, from part A that the derivative is:

[tex]\displaystyle \large{f'(x)=-x+7}[/tex]

Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:

[tex]\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}[/tex]

When f'(x) < 0 —> e.g -x + 7 < 0:

[tex]\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}[/tex]

Therefore, the function will increase when x < 7 and will decrease when x > 7.

Answer:

Choice B and Choice C

Step-by-step explanation:

Hello! This is how I solved this question:

(10 x 8 x 2) + (3 x 3 x 4) = 160 + 36 = 196ft^3

(10 x 3 x 2) + (5 x 4 x 2) = 60 + 40 = 100ft^3

(8 x 4 x 2) + (3 x 6 x 2) = 64 + 36 = 100ft^3

(8 x 10 x 3) + (4 x 5 x 2) = 240 + 40 = 280ft^3

Choice B and Choice C are the same values, and knowing that you need two of the same values for the volume of the figure must be the same. Giving you your two answers from simply multiplying and adding the answers.

Hope this helps, don't hesitate to ask if you have additional inquiries!

Answer:

Range & Isabella

Step-by-step explanation:

Part A:

Definitely not range mean or median, as that'll give you their average, not consistency.  None of their tables show any repeating values, so not mode either, and range would be the most hopeful for this.

Part B:

The results with the smallest range would be the most consistent:

Charles:
Lowest value = 39 and Highest Value = 57
Range = 57-39 = 18

Isabella:
Lowest value = 62 and Highest value = 71
Range = 71-62 = 9

Naomi:
Lowest value = 61 and Highest value = 94
Range = 94-61 = 33

Isabella achieved the most consistent results.  Hope this helps

Answer:

x = 17   degrees        y = 3  units

Step-by-step explanation:

Since angle   F  and  E are equal,   sides  DE  and  DF   are equal and you now have an equilateral triangle

  each angle is   60 degrees    so   4x - 8 = 60    shows   x = 17

   since the sides are equal :   8y-3 = 6y+3   shows y = 3  

Answer:

x = 17 , y = 4

Step-by-step explanation:

since EF and DF are congruent , then

8y - 5 = 6y + 3 ( subtract 6y from both sides )

2y - 5 = 3 ( add 5 to both sides )

2y = 8 ( divide both sides by 2 )

y = 4

--------

the triangle has 3 congruent angles , then

3(4x - 8) = 180 ( divide both sides by 3 )

4x - 8 = 60 ( add 8 to both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Answer:

[tex]\sf m = \dfrac{2}{5}[/tex]

Explanation:

A system of equations will have no solution when:

Meaning they shall have the same slope but different constant.

[tex]\sf y = \dfrac{2}{5} x - 7[/tex]       Here slope: 2/5  and constant: -7

Another equation:

[tex]\sf y = \dfrac{2}{5} x + 3[/tex]       Has the same slope but different constant.

Answer:

m = 2/5

Step-by-step explanation:

Understanding :

A system of equations have no solutions when they do not cross/intersect each other at any point.

This is only possible when the slopes of the lines are equal.

Solution :

Hence,

Solving as exponents

[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]

[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]

[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]

[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]

[tex]\\ \rm\Rrightarrow -2x=4[/tex]

[tex]\\ \rm\Rrightarrow x=-2[/tex]

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]9^{x-8}=3^{4x-12}[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]

[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 2x-16=4x-12[/tex]

Subtract 2x from both sides:

[tex]\implies 2x-16-2x=4x-12-2x[/tex]

[tex]\implies -16=2x-12[/tex]

Add 12 to both sides:

[tex]\implies -16+12=2x-12+12[/tex]

[tex]\implies -4=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies x=-2[/tex]

Answer:

the region of the graph where the shaded regions of the graph of each inequality overlap, or where the regions intersect

Step-by-step explanation:

Answer:

∠ T = 76°

Step-by-step explanation:

RSTU is a cyclic quadrilateral

the opposite angles of a cyclic quadrilateral sum to 180°

∠ T + ∠ R = 180°

∠ T + 104° = 180° ( subtract 104° from both sides )

∠ T = 76°

Answer:

I'm assuming it's sayin that u get 2 for 1.89?

Answer:

its 23, (0.63 maybe), 7 ,5,5 that’s it

Step-by-step explanation: