Which term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line?

Answer:

∠BAC = 35°

AC = 5 cm

BD = 2.4 cm

Step-by-step explanation:

As ΔABC ~ ΔBDC then ∠CBD ≅ ∠BAC

As ∠CBD = 35° then ∠BAC = 35°

Using Pythagoras' Theorem

CB² + AB² = AC²

⇒ 3² + 4² = AC²

⇒ 25 = AC²

⇒ AC = 5 cm

As ΔABC ~ ΔBDC then

AB : AC = BD : BC

⇒ 4 : 5 = BD : 3

[tex]\sf \implies \dfrac45=\dfrac{BD}{3}[/tex]

[tex]\sf \implies BD=\dfrac{12}{5}=2.4\:cm[/tex]

**A right triangle with legs of 3cm and 4cm, and a perpendicular line from the hypotenuse to the right angle vertex, does not have an internal angle CBD of 35°.  It should be 36.87°.  So if you use SOHCAHTOA to find the length of BD, it will be incorrect. See attached diagram**

Answer:

Step-by-step explanation:

Given

Corresponding angles are congruent

Use Pythagorean to find the length of AC

The ratio of corresponding sides is equal

Answer:

James has 4 red balloons

Step-by-step explanation:

16 × 1/4 = 4

You could also say 16 ÷ 4 = 4

Hope that helps!

Answer:

1.75% and 16 times

Step-by-step explanation:

Compound interest formula:

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting given values into the formula:

[tex]\sf \implies A=600(1+\frac{0.07}{4})^{4 \times4}[/tex]

          [tex]\sf =791.9576107...[/tex]

Equivalent interest rate:

[tex]\sf \implies \dfrac{r}{n}= \dfrac{0.07}{4}=0.0175=1.75 \%[/tex]

Number of times compounded:

[tex]\sf \implies nt=4 \times 4=16[/tex]

All you need to do is use your calculator to solve that equation. Just so you don't need to for just this one, here's the answer you should type into the box:

3/20

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &7\\ t=\textit{elapsed time}\dotfill &127\\ h=\textit{half-life}\dotfill &64.8 \end{cases} \\\\\\ A=7\left( \frac{1}{2} \right)^{\frac{127}{64.8}}\implies A=7\left( \frac{1}{2} \right)^{\frac{635}{324}}\implies A\approx 1.80[/tex]

The half-life of sr-85, which may be used in bone scans, is 64.8 days. 1.80 milligrams of a 7 mg sample will be left after 127 days.

Half-life is defined as the time required for a quantity to reduce to half of its initial value.

The half-life of sr-85, which may be used in bone scans, is 64. 8 days.

We need to find how many milligrams of a 7 mg sample will be left after 127 days.

[tex]\rm A = P\frac{1}{2} ^{t/h}[/tex]

here A = current amount

P = inital amount

t = time

h = half life

So,

[tex]\rm A = 7\frac{1}{2} ^{127/64.8}[/tex]

[tex]\rm A = 7\frac{1}{2} ^{635/324}\\A = 1.80[/tex]

Learn more about half-life;

https://brainly.com/question/24710827

#SPJ4

Answer:

the volume should be 9.42

Answer:

8 and yes

Step-by-step explanation:

c² - b² = a²

100 - 36 = a²

64 = a²

a = 8

the three sides form a sequence, 6, 8, 10, which is the pythagorean triple.

A 2 x 2 matrix has 2 rows and 2 columns

A specific 2 x 2 matrix a with no zero entries at all is [tex]\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right][/tex]

From the question, we understand that the matrix is a 2 x 2 matrix.

A 2 x 2 matrix is represented as:

[tex]\left[\begin{array}{cc}a&b\\c&d&\end{array}\right][/tex]

Also from the question we understand that the elements of the matrix are non-zero.

This means that:

[tex]a \ne 0\ , b \ne 0, \ c \ne 0, \ d \ne 0[/tex]

An example of such matrix is:

[tex]\left[\begin{array}{cc}1&-2\\-3&6&\end{array}\right][/tex]

Note that there are several matrices that fit the given construction requirement

Read more about matrix at:

https://brainly.com/question/1821869

Answer:

120 miles/hour

Step-by-step explanation:

6 x 10= 60 min

12 x 10= 120 miles

Answer:

Definitely 120 miles per hour.

Step-by-step explanation:

First, if she drove 50,000,000 fast, you need to do 6 minutes x 10 because 10 can go into 50,000,000. So, yes, it's 60. But that isn't right... it's too short. Try the next one.

How about we do the miles. 12 miles x 10 will get you your answer; 120.

I honestly don't know what I'm doing. It most likely isn't 120, but I did the math, and it was hard.

Answer:

Supplementary angles are two angles whose sum is equal to 180∘. In other words when you add the measure of one angle in the pair with the other angle in the pair, they equal 180 degrees. These two angles are supplementary because together they form a straight line.Jun 5, 2017

Step-by-step explanation:

Luna~

Answer:

4/24,,,5/24,,7/24

hope it helps u

0.595

= 595/1000

= 119/200

Using the normal distribution, it is found that the probability is 0.16.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given by, respectively, [tex]\mu = 70, \sigma = 3[/tex].

The proportion of students between 45 and 67 inches is the p-value of Z when X = 67 subtracted by the p-value of Z when X = 45, hence:

X = 67:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{67 - 70}{3}[/tex]

Z = -1

Z = -1 has a p-value of 0.16.

X = 45:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{45 - 70}{3}[/tex]

Z = -8.3

Z = -8.3 has a p-value of 0.

0.16 - 0 = 0.16

The probability is 0.16.

More can be learned about the normal distribution at https://brainly.com/question/24663213

Answer:

2x + y = 5

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - 2x + 5 ( add 2x to both sides )

2x + y = 5 ← in standard form

Answer:

 y=-2x+5 as standard form is 2x+y=5

Cindy's new annual premium including the discount would be given by: Option A: $504.24

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

The table given is:

Type of Insurance Coverage  Coverage Limits  Annual Premiums

Bodily Injury                              $50/100,000          $31. 75

Property Damage                     $25,000                 $120. 50

Collision                                    $500 deductible    $275. 75

Comprehensive                        $100 deductible     $100. 00

Her total annual premium = 31.75 + 120.50 + 275.75 + 100 = $528

Discount offered to her = 4.5% of $528 = [tex]\dfrac{528}{100} \times 4.5 = 23.76[/tex] (in dollars)

The new premium that she needs to pay after discount = Old premium - discount = $528 - $23.76 = $504.24

Thus, Cindy's new annual premium including the discount would be given by: Option A: $504.24

Learn more about percent here:

https://brainly.com/question/11549320

Answer:

its a

Step-by-step explanation:

Answer:

d=8

Step-by-step explanation:

4.5(8)>31.5 works because 36>31.5

The area of the sector of the circle will be 759.34 m². It is the amount of area enclosed inside the sector's perimeter.

The area of a circle's sector is the amount of space encompassed inside the sector's perimeter. The origin of a sector is always the circle's center.

The region of a circle encompassed by its two radii and the arc connecting them is known as the sector of a circle.

The given data in the problem is;

[tex]\rm \theta[/tex] is the central angle=[tex]\frac{10\pi}{7}[/tex]= 4.485

r is the radius = 18.4 m

The area of a sector of a circle is found as;

[tex]\rm A= \frac{\theta}{2} \pi r^2 \\\\ \rm A= \frac{4.485}{2} \times (18.4)^2 \\\\ \rm A=759.34 \ m^2[/tex]

Hence the area of the sector of the circle will be 759.34 m².

To learn more about the area of the sector refer to the link;

https://brainly.com/question/1582027

Answer:

Step-by-step explanation:

Answer:

Real solutions

Step-by-step explanation:

I know that because I am smart

======================================================

Perpendicular lines have slopes that are opposite reciprocals.

This means we take the slope, flop it over, and change its sign.

In this case, we have

[tex]\boxed{-4}[/tex]

First, flop it over:

[tex]\boxed{-\frac{1}{4}}[/tex]

Change its sign:

[tex]\boxed{\frac{1}{4}}[/tex]

Now, let's write the equation of the line in point-slope form:-

[tex]\bigstar\boxed{\pmb{y-y1=m(x-x1)}}\longleftarrow\sf{Point-Slope~Formula}[/tex]

Where

y₁ is the y-coordinate of the point that the line intersects

m is the slope of the line

x₁ is the x-coordinate of the point that the line intersects

In this case,

y₁ is equal to -4

m is equal to  [tex]\boxed{\frac{1}{4} }[/tex]

x₁ is equal to -2

Plug in the values:-

[tex]\bigstar{\boxed{y-(-4)=\frac{1}{4}(x-(-2)}[/tex]

Simplify:-

[tex]\longrightarrow\sf{y+4=\frac{1}{4} (x+2)[/tex]

and we're done!

===========================================================

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Step-by-step explanation:

Answer:

x< -6 or x > 0 (C is correct for question 1.) x ≤  2  (C is correct for question 2)

Step-by-step explanation:

You have given me 2 questions:

| x + 3 | + 7 > 10

3x + 6 ≤ 12

Let's solve the first one:

| x + 3 | + 7 > 10

Before we start, the greater-than sign means that the point on the number line has to not be filled in.

| x + 3 | + 7 > 10        

**Along with this equation you need to do a negative one meaning you need to flip the sign to a less than one and make 10 and 7 negative.

| x + 3 | - 7 < -10

| x + 3 | + 7 > 10

**Notice that this one is the original one.

Subtract 7 both sides

| x + 3 | > 10 -7

Now do 10-7

| x + 3 | > 3

Now subtract 3 both sides

x > 0

The negative case:

| x + 3 | - 7 < -10

Add 7 both sides

| x + 3 | < -10 + 7

Do -10 + 7

| x + 3 | < -3

Subtract 3 both sides

x < -3-3

Solve -3-3

x < -6

Your inequalities:

x< -6 or x > 0

The or statement is for greater than and the "and" is for less than.

Answer Choice C is correct.

Next Question:

3x + 6 ≤ 12

**Before we do anything, we have a less than or equal sign**

The point will be filled on the number line.

This is a typical inequality two-step:

3x + 6 ≤ 12

Subtract 6 from both sides

3x ≤ 12-6

Do 12-6

3x ≤ 6

Now divide 6 by 3

x ≤  2  

Answer Choice C is correct.

So the function is

[tex]\\ \rm\rightarrowtail y=4.5x^2[/tex]

As we know

hence domain is

[tex]\\ \rm\rightarrowtail D_f\in R[/tex]

Hence range:-

[tex]\\ \rm\rightarrowtail R_f\in [0,\infty)[/tex]

Answer:

400

Step-by-step explanation:

you can do 2x2 and you get 4 then add the zeros

Answer:

3/12 + 239/12 = 20.16...

2309/23 + 32/32= 101.39

34/234 + 349/234=1.64

23/23-11/23= 0.52

57/78-32/78 = 0.32

Step-by-step explanation:

Just divide both sides first and then add, so it is easier to get your answer.

My answers are all rounded or repeated.

I hope this helps!

-No one

Answer/Step-by-step explanation:

3/12 + 239/12

3 + 239 = 242

242/12 = 20 1/6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Find common multiplier

2309/23 + 32/32

Add

2332/23

Mixed Fraction

101 9/23

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

34/234 + 349/234

23 + 349 = 383

383/234

Mixed Fraction

1 149/234

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

23/23-11/23

23 - 11 = 12

12/23

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

57/78 - 32/78

57 - 32 = 25

25/78

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

Using the percentile concept, it is found that the maximum age of the youngest 25% of the passengers is of 30.

When a measure is in the xth percentile of a data-set, it is greater than x% of the measures and lesser than (100 - x)%.

Researching the problem on the internet, it is found that the distribution of the ages is described by a box and whisker plot, which states that:

Hence, the maximum age of the youngest 25% of the passengers is of 30.

More can be learned about the percentile concept at https://brainly.com/question/24495213

Answer:

  A.  m^2+7m+10=0

Step-by-step explanation:

This is a problem in pattern matching, and in substituting a variable for a pattern.

  (x^2+3)^2 +7x^2 +21 = -10 . . . . . . given

  (x^2 +3)^2 +7(x^2 +3) = -10 . . . . . factor the last two terms

  m^2 +7m = -10 . . . . . . . . . . . . subsitute m for x^2 +3

  m^2 +7m +10 = 0 . . . . . . . . add 10 to both sides; matches A

well, when we use the word "the function" we're referring to the dependent part, which depends on the independent, y,x wise, we're referring to the function "y" or f(x) if you wish.

so for an exponential function

is the function ever positive only? it can be

is it negative only?  it can be

can it be both?  sure thing, most of the time it's both

we can say a function f(x) is always positive when the independent values of "x" yield a positive value only, mind you that when we're talking about "the function" we're really referring to the resulting values in a set, so can the values of the output no matter what "x" we use be always positive? sure, can they also be negative only? sure, how about both? sure thing.

notice the template in the picture below, we can transform any exponential function like the one above 2ˣ with some vertical shift upwards, and is always positive, or -2ˣ with a vertical shift downwards and it's always negative, or we can stretch it about and have -2ˣ shifted upwards so sometimes is positive, and sometimes is negative.

above the x-axis is always positive, below is negative, but with transformations on the parent function it can be any of the three types.