allison drove home at 58 mph, but her brother austin, who left at the same time, could drive at only 46 mph. when allison arrived, austin still had 24 miles to go. how far did allison drive?

Given the expression:

We start from the parenthesis inside the brackets. We know that 3-2=1, then:

now, we have that 10^2=100 and 2*11 =22, then:

therefore, the result of simplifying the expression is 78

Answer:

1133.98

almost 1134 grams :)

Step-by-step explanation:

multiply by 28.35 to get the answer :)

Answer:

1133.98

Step-by-step explanation:

Hope it helps and have a nice day!!!!! :)

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The height, h of the parallelogram is 4 feet.

A parallelogram is a quadrilateral with opposites sides equal to each other. Opposite sides of a parallelogram are also parallel to each other.

Opposite angles of a parallelogram are congruent. The consecutive or adjacent angles of a parallelogram is supplementary.

Therefore, the height of the parallelogram can be found as follows:

The sum of angles in a parallelogram is 360 degrees.

Hence,

sin ∅ = opposite / hypotenuse

where

sin ∅ = 3 / 6

sin ∅ = 1 / 2

∅ = sin⁻¹ 0.5

∅ = 30

Therefore,

30 + 30 + 2x = 360

where

60 + 2x = 360

2x = 360 - 60

2x = 300

x = 300 / 2

x = 150

Let's find the height of the parallelogram using trigonometric ratios,

sin 30° = h / 8

cross multiply

h = 8 sin 30°

h = 8 × 0.5

Therefore,

h = 4 ft

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In triangle  ABC, BC = 29 units.

Given,

In Δ ABC, ∠A = 45°.

A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.

Let altitude meet AB on D.

So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°

In ΔADC,

tan A = DC/AD

tan 45° = DC/20

          1 = DC/20

      DC = 20 units

In ΔBDC,

BC² = BD² + DC²     (Pythagorean Theorem)

      = 21²  + 20²

      = 441 + 400

      = 841

BC  = √841

      = 29  

Hence, BC = 29 units.

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Answer:

x = 113

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 8 , then

sum = 180° × 6 = 1080°

sum the interior angles and equate to 1080

x + 137 + 144 + 139 + 123 + 150 + 142 + 132 = 1080

x + 967 = 1080 ( subtract 967 from both sides )

x = 113

The length of the incline of the ramp will be [h] = 12.0415 ft

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -

h² = p² + b²

Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.

From the data given, we can consider the ramp construction as right angled triangle. We can write -

base [b] = 12 ft

height [p] = 1 ft

Using the Pythagoras theorem -

h² = (12 x 12) + (1 x 1)

h² = 144 + 1

h = √145

h = 12.0415

Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft

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The rate of the slowest car is 86 km/hr using the concept of relative velocity.

Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.

Let the speed of 1st car is v₁.

Let the speed of 2nd car is v₂.

v₁- v₂ = 18 km/hr --- (1)

And using the concept of relativity.

S(rel) = D(rel)/time

S(rel) = 360 / 2

S(rel) = 190

v₁ + v₂ = 190 --- (2)

Adding equations 1 and 2 we get

v₁ = 104 km/hr

v₂ = 86 km/hr

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We are told that Julia keeps 255 masks on the wall and 45 on the display case, this means in total the number of masks she has is

The number of masks Julia keeps on the wall is 255 masks; therefore, the percentage of fo masks on the wall is

Hence, Julia keeps 85% of her mask collection on her wall.

Answer:

Acute scalene triangle.

More Information:

Sides: a = 10   b = 11   c = 12

Area: T = 51.521

Perimeter: p = 33

Semiperimeter: s = 16.5

Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad

Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad

Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad

Height: ha = 10.304

Height: hb = 9.367

Height: hc = 8.587

Median: ma = 10.368

Median: mb = 9.579

Median: mc = 8.631

Inradius: r = 3.122

Circumradius: R = 6.405

Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]

Centroid: CG[5.708; 2.862]

Coordinates of the circumscribed circle: U[6; 2.242]

Coordinates of the inscribed circle: I[5.5; 3.122]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad

∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad

∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad

How to Solve:

The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

1. Input data entered: sides a, b, and c.

a=10

b=11

c=12

We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.

a=10

b=11

c=12

2. The triangle perimeter is the sum of the lengths of its three sides

3. Semiperimeter of the triangle

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

4. The triangle area using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

5. Calculate the heights of the triangle from its area.

There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.

6. Calculation of the inner angles of the triangle using a Law of Cosines

The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.

7. Inradius

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

8. Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

9. Calculation of medians

A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.

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The triangles are similar. The smaller is isosceles, so the 3 of them are as well.

Let's Start by finding the hypotenuse of the smaller one:

a² = 2

Answer:negative

Step-by-step explanation:

Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.

From the given values, we can see that the lowest values is -32 and the highest value ie -4. Since the range is the difference betwwwn the highest and the lowest value, the range is

On the other hand, the sample variance formula is

where x^bar is the mean and n is the total number of sample elements. In our case, n=7 and the mean is

Then, the sample variance is given by

Since the standard deviation is the square root of the sample variance, we have

By rounding the solutions to the nearest tenth, the answers are:

Looking at the graph

we have that

Decreasing intervals are

(-infinite, -2.5) and (1.75, infinite)

so

Verify each option

A ----> is true

B ---> is not true

C ---> is true

D ---> is not true

486lb of grass seed is required to cover the field on the right.

The area of Rectangle is length times of width

Let us find the areas of two rectangle larger and smaller.

Area of the larger rectangle:

60×90=5400 square feet.

Now divide the larger square area by the smaller square area:

Area of the smaller rectangle

40×50=200 square feet.

Now divide larger rectangle with smaller

5400/200 =27

27 is the ratio of the difference

27×18=486 lb.

Hence 486lb of grass seed is required to cover the field on the right.

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Answer:

104 children and 195 adults

Step-by-step explanation:

let a represent number of adults and c represent number of children , then

a + c = 299 → (1)

7a + 2c = 1573 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate c

- 2a - 2c = - 598 → (3)

add (2) and (3) term by term to eliminate c

5a + 0 = 975

5a = 975 ( divide both sides by 5 )

a = 195

substitute a = 195 into (1) and solve for c

195 + c = 299 ( subtract 195 from both sides )

c = 104

104 children and 195 adults were admitted

Answer:

height = 12

Step-by-step explanation:

try and use the formula to plug it in and solve for x.

Let

number of children admitted = x

number of adult admitted = y

Total number admitted = 335

number of children = 160

number of adult = 175

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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Answer:

x = 8 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

computation just means to calculate

x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )

x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]

rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3

= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL

= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]

= [tex]\frac{24+12\sqrt{3} }{3}[/tex]

= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]

= 8 + 4[tex]\sqrt{3}[/tex]

Answer:

2 times 1/4 = 1/2 or 0.5

Step-by-step explanation:

Step 1: Setup

First of all, note that 2 is the same as 2/1 since 2 divided by 1 is 2. Therefore, start by setting up the problem like this:

2/1 x 1/4

Step 2: Multiply

Multiply the numerators together (2 x 1 = 2) and multiply the denominators together (1 x 4 = 4) and make it into one fraction like so:

2/4

Step 3: Minimize

The greatest common factor of 2 and 4 is 2. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get the answer as follows:

1/2

Answer:x-intercepts (5,0)

y-intercepts (0,-5)

Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm

Define Dimension

A measurable extent of a particular kind, such as length, breadth, depth, or height.

Let,

T = how taller the poster is

W = how wide the poster is

According to question given,

T = W + 25  ---eq(i)

The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,

5 * (2 (T + 10)) + 5 * (2 * W) = 1350

Now substitute the eq(i) value,

5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350

Now, solve for W,

5 * (2W +50 + 20) + 10W = 1350

10W + 5(70)+ 10W = 1350

20W + 350 = 1350

20W = 1350 - 350

20W = 1000

W = 1000/20

W = 50

Now, put the W value in eq(i)

T = 50 + 25

T = 75

Therefore, The dimension are 75 * 50  i.e, Width = 50 cm , Length = 75 cm

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Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.

Given that,

Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.

This is how the equation can be rewritten:

The first equation is written as 1/8 x3y + 7/8 xy2.

It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.

Equation two:

1/4x.y.4x2 + 28y

1/4 .4 x³ .y + 28y

x3.y + 28y equation to be solved

Using the formula

y = (x3 + 28).

Third claim:

1/4. x. y. x2 + 7y

Fix the problem.

1/4 . x³ .y + 7y

Write y = (1/4x3 + 7) in a new way.

Fourth assertion:

1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x

After removing the common element x(1/8 x2y3+ 7), rewrite the equation.

Fifth Declaration

1/8 x. y. x² + 7y

1/8 x³. y + 7y

Equation y (1/8 x3 + 7) is rewritten.

Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.

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The intensity of the dishwasher will be 44.44 times the maximum intensity.

Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that area. Mathematically, we can write the intensity of sound as -

[tex]\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c[/tex]

Given is the sound intensity as measured in decibels and its measurement for a dishwasher is 37 decibels.

The given formula is -

db = 10 log(I/I₀)

Substituting the values, we get -

37 = 10 log(I/I₀)

log(I/I₀) = (37/10)

log(I/I₀) = (37/10)

(I/I₀) = e ^ (37/10)

I/I₀ = 40.44

I = 40.44I₀

Therefore, the intensity of the dishwasher will be 44.44 times the maximum intensity.

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r > -1

Negative eighty times r is less than 80 is expressed mathematically as;

Divide both sides by -80.

Note the change in sign when divided by a negative value

Answer:

x = -7

Step-by-step explanation:

Hi!

Ok we know a few things here :

x + 37 + x + 67 + 90 = 180

2x + 104 = 90

2x = -14

x = -7

Hope this helps!

Have a great day! :)

Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below

Answer:

0

Step-by-step explanation:

A painter has three partially filled paint cans.

The first contains 1 7/8 gallons

The second contains 1 1/5 gallons

The third contains 1 3/4 gallons

The total amount of paint is the sum of these paint cans.

Now let us add these mixed fraction numbers

As you can see, 4.825 is closest to 5.

Therefore, the correct option would be D