what is -3x + 7 = -1 nice if step by step explanation what is x

Answer:

Part A

Cone

[tex]\mathsf{volume \ of \ a \ cone=\dfrac13\pi r^2h}[/tex]

(where r is the radius and h is the height)

Given:

[tex]\implies \mathsf{volume \ of \ the \ cone=\dfrac13\pi \cdot a^2\cdot2a=\dfrac23\pi a^3}[/tex]

Hemisphere

[tex]\mathsf{volume \ of \ a \ sphere=\dfrac43\pi r^3}[/tex]

[tex]\implies \mathsf{volume \ of \ a \ hemisphere=\dfrac12 \cdot\dfrac43\pi r^3=\dfrac23\pi r^3}[/tex]

Given

[tex]\implies \mathsf{volume \ of \ the \ hemisphere=\dfrac23\pi a^3}[/tex]

Therefore

volume of cone with radius a = volume of hemisphere with radius a

Part B

[tex]6.82^2\times\sqrt[3]{0.005}[/tex]

Take log of base 10:

[tex]\implies \log_{10}(6.82^2\times\sqrt[3]{0.005})[/tex]

Using log law [tex]\log(a \times b)=\log a+\log b[/tex]:

[tex]\implies \log_{10}(6.82^2)+\log_{10}(\sqrt[3]{0.005})[/tex]

Using low law [tex]\log(a^b)=b \log a[/tex]

[tex]\implies 2\log_{10}(6.82)+\dfrac13\log_{10}(0.005)[/tex]

Log tables

The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.

The mantissa is found using the log tables and is always prefixed by a decimal point.

The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number

Use the log tables to find [tex]\log_{10}(6.82)[/tex]:

6.82 = 6.82 × 10⁰

⇒ characteristic = 0

log table:  row 68, column 2 ⇒ mantissa 8338 ⇒ 0.8338

characteristic + mantissa = 0 + 0.8338 = 0.8338

Therefore, [tex]\log_{10}(6.82)=0.8338[/tex]

Use the log tables to find [tex]\log_{10}(0.005)[/tex]:

[tex]0.005 = 5.0 \times 10^{-3}[/tex]

⇒ characteristic = -3

log table: row 50, column 0 ⇒ mantissa 6990 ⇒ 0.6990

characteristic  + mantissa = -3 + 0.6990 = -2.301

Therefore, [tex]\log_{10}(0.005)=-2.301[/tex]

Therefore,

[tex]2\log_{10}(6.82)+\dfrac13\log_{10}(0.005)[/tex]

[tex]\implies 2\cdot0.8338 + \dfrac13 \cdot -2.301[/tex]

[tex]\implies 1.6676 - 0.767[/tex]

[tex]\implies 0.9006[/tex]

Therefore,

[tex]\log_{10}(6.82^2\times\sqrt[3]{0.005})=0.9006[/tex]

Using [tex]\log_{a}b=c \implies a^c=b[/tex]

[tex]\implies 6.82^2\times\sqrt[3]{0.005}=10^{0.9006}[/tex]

[tex]\implies 6.82^2\times\sqrt[3]{0.005}=7.954[/tex]

given for cone:

volume of cone:

[tex]\sf \rightarrow \dfrac{1}{3} \pi r^2h[/tex]

[tex]\sf \rightarrow \dfrac{1}{3} \pi (a)^2(2a)[/tex]

[tex]\sf \rightarrow \dfrac{2\pi a^3}{3}[/tex]

no metal wasted means no volume wasted while melting so volume: same.

volume of hemisphere:

[tex]\hookrightarrow \sf \dfrac{2}{3} \pi r^3[/tex]

This is equal to the volume of cone.

[tex]\hookrightarrow \sf \dfrac{2}{3} \pi r^3 = \dfrac{2\pi a^3}{3}[/tex]

[tex]\hookrightarrow \sf a^3 = r^3[/tex]

[tex]\hookrightarrow \sf a = r[/tex]

Therefore shown that radius of cone is similar to radius of hemisphere.

(b)

[tex]6.82^2 *\sqrt[3]{0.005}[/tex]

[tex]7.9535[/tex]

[tex]7.95[/tex]

The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 3% per year compounded 12 times per year over 1 years is $103.04.

Given data

A = P + I where

P (principal) = $100.00

I (interest) = $3.04

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 100.00(1 + 0.03/12)^(12)(1)

A = 100.00(1 + 0.0025)^(12)

A = $103.04

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Answer:

C. (5,7)

Step-by-step explanation:

One endpoint at 1,3 and the midpoint at 3,5Your answer would be to as two to each the x and y of the midpoint. So the answer would be 5,7.

i) 15 students

ii) 15 students

Answer:

0.6 multiply by 5250

its 3168

The Conversion of 0.6 miles is equal to 3,168 feet.

To convert 0.6 miles to feet, we need to use the conversion factor that 1 mile is equal to 5,280 feet.

As, 1 mile= 5280 feet

So, we can multiply 0.6 miles by the conversion factor:

= 0.6 miles x 5,280 feet/mile

= 3,168 feet

Therefore, 0.6 miles is equal to 3,168 feet.

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Answer:

y = -5x - 1

Step-by-step explanation:

To find the function rule:

We use the equation "y = mx + b"

Function rule: What we need to do to "x" to get "y"

Look at the x-values. You need to know if they are going up by one or if they are skipping.  In this case, they are going up by one.

Next, look at the y-values and see how they are changing. The y-values in this table are going down by 5 every time, which means we will multiply each "x" by "-5".

After that, pick the first 'x" in the table and multiply it by "-5", then figure out what you need to do to make it equal the y-value.

You need to subtract 1. This means the rule is "y = -5x - 1"

To check if this is correct, we do the following:

y = -5x - 1

Substitute the first x and y values into the equation

9 = -5(-2) - 1

Multiply -5 and -2

9 = 10 - 1

Subtract 1 from 10

9 = 9

True

Let's check the second equation

y = -5x - 1

Substitute the x and y values in the second column of the table

4 = -5(-1) - 1

Multiply -5 and -1

4 = 5 - 1

Subtract 1 from 5

4 = 4

True

So, the function rule "y = -5x - 1" is true

Answer:

I think it is dividing the numbers by 2

Step-by-step explanation:

Although it is right,

The rule is that we stop factoring, if we can't factor out a constant that isn't 1.

In your example, we can still factor out-1.

The factorization 2x(-7-6x) is not wrong because distributing the outer 2x to each term inside gets us

which leads back to -14x-12x^2

Therefore, 2x(-7-6x) = -14x - 12x^2 is true.

Convention usually has us pull out the negative so the terms inside are all positive. This is just a practice done. There technically isn't any right way vs wrong way to factor, when we compare the two different factorizations. I think it's more of a subjective style than anything.

Answer:

#1) A

#2) B

#3) C

#5) A

#7) D

#10) D

#11) D

#14) A

#15) D

#16) A

#19) D

Step-by-step explanation:

#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:

m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2

Between the second two points,

m=(4-1)/(5-3) = 3/2

Between the third pairs of points,

m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.

#2) Substituting 4 for y and 1 for x,

y = (x+1)²

4 = (1+1)² = 2²

9 = (1+2)² = 3²

16 = (1+3)² = 4²

This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:

m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have

3=(d-5)/(4-2)

3=(d-5)/2

Multiply both sides by 2:

3*2 = ((d-5)/2)*2

6 = d-5

Add 5 to both sides:

6+5 = d-5+5

11 = d

#11) Using point slope form,

y-y₁ = m(x-x₁)

y-1 = 3(x--2)

y-1 = 3(x+2)

Using the distributive property,

y-1 = 3*x + 3*2

y-1 = 3x + 6

Add 1 to both sides:

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

y=3x+7

#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.

#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.

#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.

i hope this work for you

and sory if im wrang

12%

22 + 16 = 38

38 - 32 = 6

6 / 50 = 12 / 100 = 12%

Answer:

66.67

Step-by-step explanation:

So if 69 is 100 percentage then we need to know; x. so x% is 46 then you turn that information into this equation.  100%/x%=69/49 so then you can solve that x is 66.67. So It is 66.67%

Step-by-step explanation:

1 1/4

is also 5/4

5/4 * 3 * 1/2 * 40 =

answer in comments

please mark as brainest

Answer:

SAS I believe or CPCTC depending if that is what you are working on.

Step-by-step explanation:

Answer:

Alan = $6525

Betty = $8700

Carol = $10875

Step-by-step explanation:

Ratio of Investment is:

Alan: Betty: Carol = 3:4:5

Total profit will be divided into 12 portions (3+4+5=12)

Total profit = $26,100

One portion = $26,100/12 = $2175

Alan gets = 2175*3= 6525

Betty gets =2175*4= 8700

Carol gets = 2175*5 = 10875

Answer:

D'(2,0), E'(3,3), F'(6,4)

Step-by-step explanation:

The matrix transformation of ΔDEF for a translation 1 unit right and 2 units down for the coordinates D(3, −2), E(4, 1), and F(7, 2) will be D'(2,0), E'(3,3), F'(6,4).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that, the coordinates of ΔDEF will be D(3, −2), E(4, 1), and F(7, 2).

For a translation 1 unit right and 2 units down we got the coordinates as D'(2,0), E'(3,3), and F'(6,4).

Thus, the matrix transformation of ΔDEF for a translation 1 unit right and 2 units down for the coordinates D(3, −2), E(4, 1), and F(7, 2) will be D'(2,0), E'(3,3), F'(6,4).

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Answer:

6.2

Step-by-step explanation:

pretty sure this is the answer-- ^^

The mean of the given data set  {6, 11, 5, 2, 7} is 6.2.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

Data set= {6, 11, 5, 2, 7}

Now,

To find the mean of a data set, you need to add up all the values and divide by the number of values.

In this case, there are 5 values in the data set: 6, 11, 5, 2 and 7.

To find the mean, follow these steps:

Add up all the values: 6 + 11 + 5 + 2 + 7 = 31

Divide by the number of values: 31 / 5 = 6.2

Therefore, by the mean the answer will be 6.2.

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Answer:

28+16=44

Step-by-step explanation:

point of correction it has been solved correctly

when subtracting 44 - 16 it gives you 28

=> 44 - 16

=> 28

SO IN ORDER TO CHECK IF THE PROBLEM WAS SOLVE CORRECTLY

you will minus 28 from one of the numbers before the equal sign

the correct option is 28 + 16 equals to 44

=> 28+16=44

Solution:

Let the missing angle be x.

It should be noted:

This means that...

Combine like terms.

Subtract 44 both sides.

Simplify the RHS

Divide 2 both sides.

Answer:

68°

Step-by-step explanation:

Remember :

Solving :

Answer:

8

Multiply 0.25 by 8 ⇒ 2 [tex]in.[/tex]

I hope this helps!

Answer:

97

Step-by-step explanation:

4^2+3(37-(2*5))

4^2+3(37-10)

4^2+3(27)

16+3(27)

16+81

=97

Answer:

Step-by-step explanation:

(2*5)=10, 37-10=27, 4^2=16, 3(27)=81, 16+81= 97

Answer:

40°

Step-by-step explanation:

m∠DGE = mDE/2 = 80/2 = 40°

Answer:

3/5

108

Step-by-step explanation:

Let there are 3x goldfish, then 2x belta fish

total 3x + 2x = 5x fish

so 3x/5x = 3/5 are goldfish.

total fish = 5x = 180, so x = 180/5 = 36

The store has 3x = 3*36 = 108 goldfish.

Answer:

x = 10√2

Step-by-step explanation:

Value Of X:

the value of x is 10√2 (A)

Answer:

3/4

Step-by-step explanation:

Opposite sides of a parallelogram are congruent

6y +3 = 10y

3 = 4y

[tex]\frac{3}{4}[/tex] =  y

Answer:

DOMAIN : x ∈ (-∞ , -3 )U (4 , ∞) or {x | x ∈ R where x ≠ -3 and 4}

REAL ZEROS : x = 5/3

Step-by-step explanation:

[tex]f(x) = \frac{3x -5}{x^{2} -x-12}[/tex]

factorize the bottom part

[tex]x^{2} - x - 12[/tex]

product = -12 , sum = -1 , factors = -4 and 3

[tex]x^{2} +3x-4x-12=0[/tex]

x (x + 3) - 4(x + 3) = 0

(x - 4) ( x + 3) = 0

x - 4 = 0 and x + 3 = 0

x = 4 and x = -3

for the function f(x) the domain is all real numbers ( R ) except - 3 and 4

Domain = x ∈ (-∞ , -3 )U (4 , ∞)

TO FIND THE ZEROS LET f(x) be equal to zero

[tex]0 = \frac{3x - 5}{x^{2} - x - 12}[/tex]

cross multiply

0 = 3x - 5

find x

3x = 5

[tex]x = \frac{5}{3}[/tex]