a test is worth 100 points each problem is worth either 2 points or 5 points the number of 5 point problems is22 less than the number of 2 point problems how many problems of each type are on the test

When a line L is perpendicular to two lines on the plane that intersects line L , then line L is perpendicular to the plane.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90° (right angle)

Perpendicular lines are intersecting lines.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

When a line is perpendicular to two lines on the plane then it is perpendicular to the plane.

We can say that when the line L is perpendicular to every line in the plane that intersects line L, then we can say that a line and a plane are perpendicular.

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Answer: 20.15

Step-by-step explanation:

First, make the percentage into an actual number. So divide 65 by 100 (because percent is based off of 100) which gives you 0.65. Then multiply 0.65 by 31 which gives you 20.15. Have a good day ;)

The multiplicative inverse of 'a' is assure by a-1 or 1/a. on other side, the multiplicative inverse of a number is present as 1 divided by the number.

The multiplication inverse of 3/7 is 7/3.

hence, the multiplicative inverse of -3/7 is -7/3 power 9.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to define mathematical expressions.

The word 'inverse' concludes something contrary/opposite in effect, order, position. or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse approach is called that the multiply of a number and its reciprocal is 1.

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Mike is correct as to make 30 batches of Raisin Nut energy bars, the bakery will use 84 cups of granola and to make 15 batches of Honey Almond energy bars, the bakery will use 63 cups of granola.

For raising, we have = 28(3) = 84 cups

For honey almond, we have = 4.2(1.5) = 63 cups

To make 30 batches of Raisin Nut energy bars, the bakery will use 84 cups of granola and to make 15 batches of Honey Almond energy bars, the bakery will use 63 cups of granola which is why Mike is considered to be correct.

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The full question is:

The table shows the number of cups of granola that a bakery uses for every 10 batches of energy bars.

Type of Energy Bar Amount of Granola (cups)

Raisin Nut 28

Honey Almond 42

Cranberry Walnut 36

Mike says that the bakery uses more granola to make 30 batches of Raisin Nut energy bars than to make 15 batches of Honey Almond energy bars.

Is Mike correct? Use the drop-down menus to explain.

Mike is Correct/Incorrect . To make 30 batches of Raisin Nut energy bars, the bakery will use 84/28/42/56 cups of granola. To make 15 batches of Honey Almond energy bars, the bakery will use 126/84/63/42 cups of granola.

The principal of interest 3415 naira, rate = 5% and time 4 yrs and 3 months​ is 4017.64 naira.

In the context of borrowing, principal refers to the initial sum of a loan; it can also refer to the balance still owed on a loan. For instance, the principal of a $50,000 mortgage is $50,000. If you pay off $30,000, the remaining $20,000 constitutes the principal balance.

The principal of a loan determines how much interest you will pay. When you pay a loan off each month, the amount first goes to pay off the interest that has accumulated; only then is the remaining amount applied to the principal. The only way to lower the monthly interest payment is to reduce the loan's principal.

given

I=3415

r=5%

time=4yrs 3 months

=4.25 yrs

we know,

p=Ix100/tr

= 3415x100/4.25x0.05

=4017.64 naira

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A parallelogram and a semicircle both have an area of 264 and 628 square metres, respectively. A = 892 is the total area.

We have a half-circle and a parallelogram.The parallelogram's area is A=basis*height. [tex]A = r^2[/tex], where r is the radius, is the formula for a circle's area (half of diameter). As a result, the half circle's area is equal to

[tex]$A=\frac{\pi r^2}{2}$[/tex]

parallelogram:

b=12

h=22

A=12 × 22

A=264

Half circle:

r=20

A=(3.14 × 20²)/2

A=628

Total Surface Area of the Figure:

A=264 + 628

A=892 .

Half of a circle's surface area makes up a semicircle. As a circle's area is [tex]r^{2}[/tex], Therefore, a semicircle's area is equal to 1/2([tex]r^{2}[/tex]), where r is its radius. 3.14, or 22/7, is the value of.

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Answer:

115

Step-by-step explanation:

The range in the following question is the set of all real numbers from 0 to 200.

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A shape that has all sides equal and all angles right angles is called a square.

In a square, all four sides are congruent (equal in length) and all four angles are right angles (90 degrees).

A square is also a special case of a rectangle, which is a four-sided polygon with opposite sides parallel and equal in length. In rectangle, all angles are right angles (90 degrees).

A square is also special case of a rhombus, which is a four-sided polygon with opposite sides parallel and equal in length, but all angles are not necessarily right angles.

A square is also special case of a parallelogram, which is a four-sided polygon with opposite sides parallel and equal in length, but all angles are not necessarily right angles.

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y = -2(x - 8)(x - 2)

y = -2(x² -2x -8x +16)

y = -2(x² - 10x + 16)

y = -2x² + 20x - 32

Answer:

y= −2x^2+20x−32

Step-by-step explanation:

y = −2(x−8)(x−2)

= - 2(x^2 - 10x +16)

= - 2x^2 - (-10x)-2. 16

= - 2x^2 +20x - 32

Answer:

The number 25 is not a prime number

Answer:

10.224 hours

Step-by-step explanation:

1 day on Earth = 24 hours

1 day on Saturn = 42.6% of 24 hours

42.6% = 0.426

24 x 0.426 = 10.224 hours

So, there are 10.224 hours on Saturn.

Answer:

Step-by-step explanation: Using data from NASA's Cassini spacecraft, researchers believe they solved a longstanding mystery of solar system science: the length of a day on Saturn. It's 10 hours, 33 minutes, and 38 seconds. i hope this helps

Answer: The total clockwise moment of the weight of the diving board and the weight of the girl at about Point A can be calculated using the equation:

moment = force x distance

In this case, the force is the weight of the diving board (800 N) and the weight of the girl (600 N) and the distance is the distance from Point A to the support (2.5m).

So the total clockwise moment is:

moment = (800 N + 600 N) x 2.5 m = 1400 N x 2.5 m = 3500 Nm

The unit for moment is Newton-meter (Nm).

It's worth noting that in this problem, the clockwise moment is calculated by considering the force and the distance in the same direction, and the moment is positive, if the force is acting in a clockwise direction.

Step-by-step explanation:

So, the slope of the given line is 2.

The slope of a line is a measure of the steepness of the line and is represented by the letter "m" in the equation of a line: y = mx + b. The slope is calculated by the ratio of the change in y to the change in x.

The equation of a line y = 2x - 10 is already in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope of the line is m = 2.

This means that for every unit increase in x, y will increase by 2 units. If we graph this line, we can see that it has a steepness of 2, which means it has a positive slope. A positive slope indicates that the line increases as we move to the right and a negative slope indicates that the line decreases as we move to the right.

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The factors or multiples of the algebraic expression, x² - 36 are (x-6) and (x+6) .

Factorization of algebraic expressions is defined as the process of finding the factors of an expression which refers to finding two or more expressions whose product is equals to that expression. Some Identities which are used to Factorize Algebraic Expressions,

(a+b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a² - b² = (a+b)(a -b) etc.

We need to factorise, p(x) = x² − 36.

The algebraic expression, p(x) can be factorised by using property, a² - b² = (a+b)(a-b). So, it can be written as x² - 6², comparing it with a² - b² , here a = x,

b = 6. Hence, (x² − 36) = (x+6)(x−6). Therefore, the required factors are (x+6)(x−6).

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An expression equivalent to (5k-3) (2k-1) is k (10 k - 11) + 3.

simplify | (5 k - 3) (2 k - 1)

Results:

1\/40 (20 k - 11)^2 - 1\/40

k (10 k - 11) + 3.

An expression equivalent to (5k-3) (2k-1) is k (10 k - 11) + 3.

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Answer:

x=2.3

Step-by-step explanation:

Isosceles triangle means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2+b^2=c^2[/tex])

[tex]x^2+x^2=\sqrt{11}^2 \\2x^2=11\\x=\sqrt{\frac{11}{2} } \\x=2.345...\\x=2.3[/tex]

Assuming all my math is right, this is your answer

Answer: The smallest critical value is -5

Step-by-step explanation:

Critical values occur at critical points(they give you important information).

In all rational functions, x-intercepts(zeros) and discontinuities need to be considered. So the critical values here are -5, -3, and -2.

Fairfax is 15.94 miles more in distance to Manchester than to Hillsboro

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance between Manchester and Newton be = 10.94 miles

Let the distance between Newton and Fairfax be = 13.57 miles

Let the distance between Fairfax and Hillsboro be = 8.57 miles

Now , the distance between Manchester and Fairfax = distance between Manchester and Newton + distance between Newton and Fairfax

Substituting the values in the equation , we get

The distance between Manchester and Fairfax = 10.94 + 13.57

The distance between Manchester and Fairfax = 24.51 miles

So , the difference between the distances A = distance between Manchester and Fairfax - distance between Fairfax and Hillsboro

Substituting the values in the equation , we get

The difference between the distances A = 24.51 - 8.57

The difference between the distances A = 15.94 miles

Hence , the distance is 15.94 miles

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The value of the acute angle theta is 59.99 degrees

From the question, we have the following parameters that can be used in our computation:

tan theta equals1.73205

Express teh equation properly

So, we have the following representation

tan theta = 1.73205

Take the arc tan of both sides

theta = tan^-1(1.73205)

Evaluate

theta = 59.99

HEnce, the acute angle is 59.99

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Answer:

∠ BAS = 122° , ∠ N = 89°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(2)

∠ BAS is an exterior angle of the triangle, then

19x + 8 = 6x + 11 + 75

19x + 8 = 6x + 86 ( subtract 6x from both sides )

13x + 8 = 86 ( subtract 8 from both sides )

13x = 78 ( divide both sides by 13 )

x = 6

Then

∠ BAS = 19x + 8 = 19(6) + 8 = 114 + 8 = 122°

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

(4)

11x + 31 is an exterior angle of the triangle , so

11x + 31 = 5x - 4 + 10x - 1

11x + 31 = 15x - 5 ( subtract 15x from both sides )

- 4x + 31 = - 5 ( subtract 31 from both sides )

- 4x = - 36 ( divide both sides by - 4 )

x = 9

Then

∠ N = 10x - 1 = 10(9) - 1 = 90 - 1 = 89°

A 90-degree tan is referred to as infinity. Thus, 90 degrees is the value for tan-1.

It is given that, tan⁻¹∞

We have to find the value of tan⁻¹∞.

Now,

The value of tan⁻¹∞ is π/2.

By using the trigonometric concepts, we can find the value of tan⁻¹∞

we already know that, tan π/2 = ∞

we have to apply tan⁻¹ on both sides

we get,

              tan⁻¹ tan π/2 = tan ∞

                             π/2 = tan⁻¹∞

Hence, the value of tan⁻¹∞ is  π/2.

The trigonometric function "tangent" is represented by the inverse function "inverse tan." The opposing side of the right triangle is divided by the adjacent side, and this relationship is utilized to compute the angle by using the tangent ratio of the angle. All inverse trigonometric functions must be named with the prefix "arc," so inverse tangent is abbreviated as "arctan."

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To simplify a complex fraction, we use the following steps:

1- Use various rules of fractions to simplify both the numerator and denominator into a simple fraction. Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator.

2- Use the following rule to evaluate the result.

3- If needed, simplify the rational expression.

A complex fraction in mathematics is one that has another fraction in either the numerator, the denominator, or both. Simplifying difficult fractions is frequently helpful when working with them. This may be accomplished by utilizing a few straightforward procedures and different fractional rules.

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Answer:

How do you calculate grams per 100mL concentration?

The concentration is the amount divided by the volume it is dissolved in. For example you might dissolve 0.9g of sodium chloride in 100mL of water. Sometimes this is referred to as 0.9% w/v since it is 0.9g weight divided by 100mL volume and “w/v” stands for weight per volume.”

Solubility≡62.5⋅g⋅100⋅mL−1..

Explanation:

☯We want Concentration=Mass of solute100 mL volume of solvent.

We make the reasonable assumption that the volume of solution is equal to 40⋅mL.

And so we set up the quotient.

25⋅g(40100)⋅mL=

☯In order to answer this question, you'll want to make use of the fact that pure water under standard conditions has a density of 1 g/ml. This means that 50 ml of pure water would have a mass of 50 grams. Therefore, we know that our sample has a 25 grams of sugar, in order for the total mass to be 75 grams.

☯The question doesn't specify what unit of concentration they prefer, so you can use the easiest, which is (mass of solute)/(volume of solvent) which in this case is 25g/50ml or .5 g/ml. If you need to write this in terms of molarity, you can use the molar mass of sugar to convert the 25g into moles and divide by .05 L, as molarity is given by (moles of solute)/(volume of solvent in liters).

☯Sugar solutions or "syrups" are used extensively in canning, and sometimes referred to as "heavy" or "light" syrups.

The terms heavy and light are commonly used in two different ways. We refer to weight when we say that an adult is heavier than a child. On the other hand, something else is alluded to when we say that one syrup is heavier than another. A teaspoon of heavy syrup would obviously weigh less than a gallon of light syrup, but heavy syrup is heavier in the sense that a given volume weighs more than the same volume of light syrup. It's interesting that a given volume of "heavy cream" actually weighs less than "light cream" (in this case, "heavy" refers to the thickness, or percent milk fat).

In "Molecular Gastronomy", Herve This (pronounced Thees) points out[2] that more precision is needed in canning recipes. Some call a heavy syrup 1 cup sugar to 2 cups water (a ratio of 0.5:1) while others refer to a medium syrup as 3-1/4 c sugar to 5 c water (a ratio of 0.65:1). The latter is actually heavier, or denser. Which is better for canning?

Step-by-step explanation:

Answer:

[tex]\left(x+5\right)^2- 33=0[/tex]

See explanation below for steps

Step-by-step explanation:

We are given the quadratic equation

[tex]x^2+10x-8 = 0[/tex]

and asked to rewrite it in the form
[tex]\left(x+a\right)^2=b[/tex]

Move 8 to the right side:
[tex]x^2+10x=8[/tex]

[tex]\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2[/tex]
[tex]\mathrm{Solve\:for\:}a,\:2ax=10x:\quad a=5[/tex]

[tex]\mathrm{Add\:}a^2=5^2\mathrm{\:to\:both\:sides}[/tex]

[tex]x^2+10x+5^2=8+5^2[/tex]

So we get the original equation as:
[tex]\left(x+5\right)^2=33[/tex]

which can be rewritten as
[tex]\left(x+5\right)^2- 33=0[/tex]

Here a = 5, b = -33

Answer:

x = 2

y = 5

Step-by-step explanation:

Brainly doesn't provide online graphing tools, so I will try to walk you through what to do.

First put both equations in slope-intercept form:

y + x = 7  →  y = -x + 7

3y - 6x = 3   →   3y = 6x + 3  →  y = 2x + 1

These are easy to graph now.  

For equation (1), place a point on the y-intercept (0,7), then draw a line with a slope of -1  (down one, over one, down one, over one, etc.).  The x-intercept is (7,0).

For equation (2), the y-intercept is point (0,1).  Draw a line with a slope of 2 (up 2, over 1, up 2, over 1, etc.)  The x-intercept is (-1/2, 0).

Where the 2 lines intersect is the solution.  They should intersect at point (2,5).

The required True options for the give equation are 2 and 3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

We have,

y = [tex]\frac{2x+5}{x-1}[/tex]

1) The function is undefined foe x= -5/2

It is false because at  x= -5/2 function is defined equal to 0.

2) The point (0, -5) lie on its graph,

To check it, Value of x in equation

y = 2(0)+5/0-1 = -5

So, this option is true.

3) The line x = 1 is asymptote

For  asymptote, denominator of function must be zero.

x - 1 = 0

x = 1

It is true

4) The function is undefined foe x=  -1

It is false because at  x= -1 function is defined equal to -3/2

Thus, True options are 2 and 3.

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The average  rate of change on the interval - 1≤ x ≤ 4 for the given equation is 7.4

What is Quadratic equation ?

Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .

Given to find the average rate of change on the interval -1<= x <= 4

for the equation y = x^2+4x+1

put x = -1 in the equation  y = x^2+4x+1

y(-1) = -1*-1 + 4(-1) + 1

= -1-4+1

= -4.

y(4) = 4*4 + 4*4 + 1

= 16 + 16 + 1

=33

average rate = y(-1) - y(4) / -1-4

= -4-33 / -5

= 37 / 5

= 7 . 4

Hence, The average  rate of change on the interval - 1≤ x ≤ 4 for the given equation is 7.4

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The relative frequency table shows the distribution of the data with respect to all 140 people.

Frequency refers to how often something occurs over a given period of time. It can be used to describe the rate of oscillations of a wave, the number of occurrences of a given event, or the rate at which a signal is processed. Frequency is typically measured in hertz (Hz), which is the number of occurrences per second. Frequency can also be expressed in terms of cycles per second (cps), revolutions per minute (rpm), or vibrations per second (vps). Frequency is an important concept in many fields such as physics, engineering, and mathematics.

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Table is attached below:

The space between the 1/3 and 1/6 is 3.83.

Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient. Division can be used to solve problems involving fractions, decimals, and percentages. It is also used to simplify complex equations and to break down large numbers into smaller, more manageable parts. Division is one of the four basic operations of arithmetic, along with addition, subtraction, and multiplication.

To calculate this, first add 3/4 and 1/3 to get 1.08, then add 1/6 to get 1.14, then subtract 1/2 to get the final answer of 3.83.

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